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Programme of Course "Mathematical Economics and Finance"



Type of course unit:

Bachelor Degree in Mathematics curriculum Generale: Elective
Master Degree in Mathematics curriculum Generale: Elective
Master Degree in Mathematical Engineering curriculum Comune: Elective

Level of course unit:

Undergraduate Degrees
Postgraduate Degrees


1st semester

Number of credits:

Master Degree in Mathematics: 6 (workload 150 hours)
Master Degree in Mathematical Engineering: 6 (workload 150 hours)
Bachelor Degree in Mathematics: 6 (workload 150 hours)


Massimiliano Giuli (massimilianodotgiuliatunivaqdotit)

1. Course Objectives

I present and organize the analytical foundations underlying modern economics and finance.

2. Course Contents and learning outcomes (Dublin Descriptors)

Topics of the course include:

  • Sperner’s lemma
  • The Knaster-Kuratowski-Mazurkiewicz lemma
  • Brouwer's fixed point theorem
  • Variational inequalities and equilibrium problems
  • Generalized monotonicity and convexity
  • Brézis-Nirenberg-Stampacchia theorem and Fan's minimax principle
  • Continuity of correspondences
  • Browder, Kakutani and Fan-Glicksberg fixed point theorems
  • Gale-Nikaido-Debreu theorem
  • Nash equilibrium of games and abstract economies
  • Walrasian equilibrium of an economy
  • An application to traffic network

On successful completion of this course, the student should

  • Know the fundamental fixed point theorems for set-valued maps and the basic existence results for equilibrium problems and variational inequalities.
  • Explain some interconnections among these various results.
  • Apply this analysis to game and economic theory

3. Course Prerequisites

I assume familiarity with vector and topological spaces, and with the standard model of the real numbers. I assume that you know the basic facts about metric spaces, normed and seminormerd spaces, Banach and Hilbert spaces.

4. Teaching methods and language


5. Assessment Methods

Written and oral

Course information last updated on: 19 gennaio 2018, 17:31